curve.go raw

   1  package x25519
   2  
   3  import (
   4  	fp "github.com/cloudflare/circl/math/fp25519"
   5  )
   6  
   7  // ladderJoye calculates a fixed-point multiplication with the generator point.
   8  // The algorithm is the right-to-left Joye's ladder as described
   9  // in "How to precompute a ladder" in SAC'2017.
  10  func ladderJoye(k *Key) {
  11  	w := [5]fp.Elt{} // [mu,x1,z1,x2,z2] order must be preserved.
  12  	fp.SetOne(&w[1]) // x1 = 1
  13  	fp.SetOne(&w[2]) // z1 = 1
  14  	w[3] = fp.Elt{   // x2 = G-S
  15  		0xbd, 0xaa, 0x2f, 0xc8, 0xfe, 0xe1, 0x94, 0x7e,
  16  		0xf8, 0xed, 0xb2, 0x14, 0xae, 0x95, 0xf0, 0xbb,
  17  		0xe2, 0x48, 0x5d, 0x23, 0xb9, 0xa0, 0xc7, 0xad,
  18  		0x34, 0xab, 0x7c, 0xe2, 0xee, 0xcd, 0xae, 0x1e,
  19  	}
  20  	fp.SetOne(&w[4]) // z2 = 1
  21  
  22  	const n = 255
  23  	const h = 3
  24  	swap := uint(1)
  25  	for s := 0; s < n-h; s++ {
  26  		i := (s + h) / 8
  27  		j := (s + h) % 8
  28  		bit := uint((k[i] >> uint(j)) & 1)
  29  		copy(w[0][:], tableGenerator[s*Size:(s+1)*Size])
  30  		diffAdd(&w, swap^bit)
  31  		swap = bit
  32  	}
  33  	for s := 0; s < h; s++ {
  34  		double(&w[1], &w[2])
  35  	}
  36  	toAffine((*[fp.Size]byte)(k), &w[1], &w[2])
  37  }
  38  
  39  // ladderMontgomery calculates a generic scalar point multiplication
  40  // The algorithm implemented is the left-to-right Montgomery's ladder.
  41  func ladderMontgomery(k, xP *Key) {
  42  	w := [5]fp.Elt{}      // [x1, x2, z2, x3, z3] order must be preserved.
  43  	w[0] = *(*fp.Elt)(xP) // x1 = xP
  44  	fp.SetOne(&w[1])      // x2 = 1
  45  	w[3] = *(*fp.Elt)(xP) // x3 = xP
  46  	fp.SetOne(&w[4])      // z3 = 1
  47  
  48  	move := uint(0)
  49  	for s := 255 - 1; s >= 0; s-- {
  50  		i := s / 8
  51  		j := s % 8
  52  		bit := uint((k[i] >> uint(j)) & 1)
  53  		ladderStep(&w, move^bit)
  54  		move = bit
  55  	}
  56  	toAffine((*[fp.Size]byte)(k), &w[1], &w[2])
  57  }
  58  
  59  func toAffine(k *[fp.Size]byte, x, z *fp.Elt) {
  60  	fp.Inv(z, z)
  61  	fp.Mul(x, x, z)
  62  	_ = fp.ToBytes(k[:], x)
  63  }
  64  
  65  var lowOrderPoints = [5]fp.Elt{
  66  	{ /* (0,_,1) point of order 2 on Curve25519 */
  67  		0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  68  		0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  69  		0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  70  		0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  71  	},
  72  	{ /* (1,_,1) point of order 4 on Curve25519 */
  73  		0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  74  		0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  75  		0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  76  		0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  77  	},
  78  	{ /* (x,_,1) first point of order 8 on Curve25519 */
  79  		0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae,
  80  		0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a,
  81  		0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd,
  82  		0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00,
  83  	},
  84  	{ /* (x,_,1) second point of order 8 on Curve25519 */
  85  		0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24,
  86  		0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b,
  87  		0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86,
  88  		0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57,
  89  	},
  90  	{ /* (-1,_,1) a point of order 4 on the twist of Curve25519 */
  91  		0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
  92  		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
  93  		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
  94  		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f,
  95  	},
  96  }
  97